Problem: Rewrite as a simplified fraction. ${0.\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 2.2222...\\ 1x &= 0.2222...\end{align*}}$ Subtracting the two equations, we have: ${9x = 2}$ ${x = \dfrac{2}{9}} $